Let $F$ be a totally real number field.
We define global $L$-packets for $\GSp(2)$ over $F$ which should
correspond to the elliptic tempered admissible homomorphisms from
the conjectural Langlands group of $F$ to the $L$-group of $\GSp(2)$ which are
reducible, or irreducible and induced from a totally real quadratic
extension of $F$.
We prove that the elements of these global $L$-packets occur in the space
of cusp forms
on $\GSp(2)$ over $F$ as predicted by Arthur's conjecture. This can be
regarded as
the $\GSp(2)$ analogue of the dihedral case of the Langlands-Tunnell
theorem. To obtain these results we prove a nonvanishing theorem for global
theta
lifts from the similitude group of a general four dimensional quadratic
space over $F$ to $\GSp(2)$ over $F$.